Systematic assessment of the quality of fit of the stochastic block model for empirical networks

TL;DR

This paper systematically evaluates how well the stochastic block model fits a diverse set of 275 empirical networks using posterior predictive checks, revealing strengths and limitations in modeling different network structures.

Contribution

It provides a comprehensive assessment of SBM fit quality across various real-world networks and suggests simple descriptors to identify when SBM is appropriate or needs extension.

Findings

SBM fits most networks well but struggles with large diameter and slow-mixing networks.

Networks with many triangles are often well modeled by SBM.

Simple descriptors can guide the applicability of SBM to different networks.

Abstract

We perform a systematic analysis of the quality of fit of the stochastic block model (SBM) for 275 empirical networks spanning a wide range of domains and orders of size magnitude. We employ posterior predictive model checking as a criterion to assess the quality of fit, which involves comparing networks generated by the inferred model with the empirical network, according to a set of network descriptors. We observe that the SBM is capable of providing an accurate description for the majority of networks considered, but falls short of saturating all modeling requirements. In particular, networks possessing a large diameter and slow-mixing random walks tend to be badly described by the SBM. However, contrary to what is often assumed, networks with a high abundance of triangles can be well described by the SBM in many cases. We demonstrate that simple network descriptors can be used to evaluate whether or not the SBM can provide a sufficiently accurate representation, potentially pointing to possible model extensions that can systematically improve the expressiveness of this class of models.